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Although the details of the instruments he used are not crucial to my story, it is worth mentioning one, called a cross-staff or radius, which Tycho had made for him early in 1564.

So Tycho worked out a table of corrections for the instrument from which he could read off the correct measurement corresponding to the incorrect reading obtained by the cross-staff for any observation he made.

Cross-staff being used for surveying and astronomy—from the title page of Petrus Apianus, Introductio geographica, 1533.

You could take two measurements in a straight line with the building and, from the distance between the measurements and the difference between the angles as measured with a cross-staff, you could calculate the height of the walls and make ladders of the right length.

You can use a cross-staff, for example, to measure the angle between the horizon and the sun at midday.